Multiple Capture in a Group Pursuit Problem with Fractional Derivatives and Phase Restrictions

Nikolay Nikandrovich Petrov
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Nikolay Nikandrovich Petrov: Laboratory of Mathematical Control Theory, Udmurt State University, 426034 Izhevsk, Russia

Mathematics, 2021, vol. 9, issue 11, 1-12

Abstract: The problem of conflict interaction between a group of pursuers and an evader in a finite-dimensional Euclidean space is considered. All participants have equal opportunities. The dynamics of all players are described by a system of differential equations with fractional derivatives in the form D ( ? ) z i = a z i + u i ? v , u i , v ? V , where D ( ? ) f is a Caputo derivative of order ? of the function f . Additionally, it is assumed that in the process of the game the evader does not move out of a convex polyhedral cone. The set of admissible controls V is a strictly convex compact and a is a real number. The goal of the group of pursuers is to capture of the evader by no less than m different pursuers (the instants of capture may or may not coincide). The target sets are the origin. For such a conflict-controlled process, we derive conditions on its parameters and initial state, which are sufficient for the trajectories of the players to meet at a certain instant of time for any counteractions of the evader. The method of resolving functions is used to solve the problem, which is used in differential games of pursuit by a group of pursuers of one evader.

Keywords: differential game; pursuer; evader; group pursuit; fractional derivatives (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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